Classical modal logic

In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators

${\displaystyle \Diamond A\equiv \lnot \Box \lnot A}$

which is also closed under the rule

${\displaystyle A\equiv B\vdash \Box A\equiv \Box B.}$

Alternatively one can give a dual definition of L by which L is classical iff it contains (as axiom or theorem)

${\displaystyle \Box A\equiv \lnot \Diamond \lnot A}$

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